I/O-optimal algorithms on grid graphs

Given a graph of which the n vertices form a regular two-dimensional grid, and in which each (possibly weighted and/or directed) edge connects a vertex to one of its eight neighbours, the following can be done in O(scan(n)) I/Os, provided M = Omega(B^2): computation of shortest paths with non-negative edge weights from a single source, breadth-first traversal, computation of a minimum spanning tree, topological sorting, time-forward processing (if the input is a plane graph), and an Euler tour (if the input graph is a tree). The minimum-spanning tree algorithm is cache-oblivious. The best previously published algorithms for these problems need Theta(sort(n)) I/Os. Estimates of the actual I/O volume show that the new algorithms may often be very efficient in practice.Comment: 12 pages' extended abstract plus 12 pages' appendix with details, proofs and calculations. Has not been published in and is currently not under review of any conference or journa

I/O-efficient strong connectivity and depth-first search for directed planar graphs

We present the first I/O-efficient algorithms for the following fundamental problems on directed planar graphs: finding the strongly connected components, finding a simple-path 2/3-separator, and computing a depth-first span-ning (DFS) tree. Our algorithms for the first two problems perform O(sort(N)) I/Os, where N = V + E and sort(N) = Θ((N/B)log M/B (N/B)) is the number of I/Os required to sort N elements. The DFS-algorithm performs O(sort(N)log(N/M)) I/Os, where M is the number of elements that fit into main memory

I/O-Efficient Algorithms on Near-Planar Graphs

Obtaining I/O-efficient algorithms for basic graph problems on sparse directed graphs is a long-standing open problem. While the best known upper bounds for most basic problems on such graphs with V vertices still require O(V ) I/Os, optimal O(sort (V )) I/O algorithms are known for special classes of sparse graphs, like planar graphs and grid graphs. It is hard to accept that a problem becomes difficult as soon as the graph contains a few deviations from planarity. In this paper we extend the class of graphs on which basic graph problems can be solved I/O-efficiently. We give a characterization of near-planarity which covers a wide range of near-planar graphs, and obtain the first I/O-efficient algorithms for directed graphs that are near-planar

Algorithmes d'approximation à mémoire limitée pour le traitement de grands graphes (le problème du Vertex Cover)

Nous nous sommes intéressés à un problème d'optimisation sur des graphes (le problème du Vertex Cover) dans un contexte bien particulier : celui des grandes instances de données. Nous avons défini un modèle de traitement se basant sur trois contraintes (en relation avec la quantité de mémoire limitée, par rapport à la grande masse de données à traiter) et qui reprenait des propriétés issus de plusieurs modèles existants. Nous avons étudié plusieurs algorithmes adaptés à ce modèle. Nous avons analysé, tout d'abord de façon théorique, la qualité de leurs solutions ainsi que leurs complexités. Nous avons ensuite mené une étude expérimentale sur de gros graphes. De manière générale, les travaux menés durant cette thèse peuvent fournir des indicateurs pour choisir le ou les algorithmes qui conviennent le mieux pour traiter le problème du vertex cover sur de gros graphes. Choisir un algorithme (qui plus est d'approximation) qui soit à la foisperformant (en terme de qualité de solution et de complexité) et qui satisfasse les contraintes du modèle que l'on considère est délicat. en effet, les algorithmes les plus performants ne sont pas toujours les mieux adaptés. dans les travaux que nous avons réalisés, nous sommes parvenus à la conclusion qu'il est préférable de choisir au départ l'algorithme qui est le mieux adapté plutôt que de choisir celui qui est le plus performant.We are interested to an optimization problem on graphs (the Vertex Cover problem) in a very specific context : the huge instances of data. We defined a treatment model based on three constraints (in connection with the limited amount of memory compared to the huge amount of data to be processed) and that reproduces properties from several existing models. We studied several algorithms adapted to this model. We examined, first theoretically, their solutions quality and their complexities. We then conducted an experimental study on large graphs. In general, the work made during this thesis may provide indicators for select algorithms that are best suited to resolve the Vertex Cover problem on large graphs. Choose an algorithm (which is approximated) that is both efficient (in terms of quality of solution and complexity) and satisfies the constraints model whether we consider is tricky. in fact, the most efficient algorithms are not always the best adapted. In the work we have done, we reached the conclusion that, at the beginning, it is best to choose the best suited algorithm rather than the more efficient.EVRY-Bib. électronique (912289901) / SudocSudocFranceF